Differentiate-fundamental-and-derived-quantities

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A Review of Jean Jacques Rousseau's 'On the Origin of Equality'

Of the fundamental tenets of "equality" today, derive from this small booklet written by the French Philosopher quantities of food, or for preparing proper housing for the winter. It could be argued that, the increase A Review of Jean Jacques Rousseau's 'On the Origin of Equality' By Johann Luther As I read through Jean Jacques Rousseau'...

Question:I was wondering if any body could explain some advanced college math classes, what they are about, how they fit in to the how spectrum of math courses, and/or why you have to take them after you complete calc 3. Ones in my college are Differential Equations 1 and 2, Linear Algebra, Modern Algebra, College Geometry, Advanced Calculus, Theory of Numbers, and Complex Variables. Only brief descriptions are given in the course catalog.

Answers:I have taken all these courses but it is just too much to type out the descriptions. Here are a couple from Wolfram...Go there and search by title. Complex analysis is the study of complex numbers together with their derivatives, manipulation, and other properties. Complex analysis is an extremely powerful tool with an unexpectedly large number of practical applications to the solution of physical problems. Contour integration, for example, provides a method of computing difficult integrals by investigating the singularities of the function in regions of the complex plane near and between the limits of integration. The key result in complex analysis is the Cauchy integral theorem, which is the reason that single-variable complex analysis has so many nice results. A single example of the unexpected power of complex analysis is Picard's great theorem, which states that an analytic function assumes every complex number, with possibly one exception, infinitely often in any neighborhood of an essential singularity! A fundamental result of complex analysis is the Cauchy-Riemann equations, which give the conditions a function must satisfy in order for a complex generalization of the derivative, the so-called complex derivative, to exist. When the complex derivative is defined "everywhere," the function is said to be analytic. Linear algebra is the study of linear sets of equations and their transformation properties. Linear algebra allows the analysis of rotations in space, least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and engineering. Confusingly, linear algebra is not actually an algebra in the technical sense of the word "algebra" (i.e., a vector space over a field , and so on). The matrix and determinant are extremely useful tools of linear algebra. One central problem of linear algebra is the solution of the matrix equation for . While this can, in theory, be solved using a matrix inverse other techniques such as Gaussian elimination are numerically more robust. In addition to being used to describe the study of linear sets of equations, the term "linear algebra" is also used to describe a particular type of algebra. In particular, a linear algebra over a field has the structure of a ring with all the usual axioms for an inner addition and an inner multiplication together with distributive laws, therefore giving it more structure than a ring. A linear algebra also admits an outer operation of multiplication by scalars (that are elements of the underlying field ). For example, the set of all linear transformations from a vector space to itself over a field forms a linear algebra over . Another example of a linear algebra is the set of all real square matrices over the field of the real numbers.

Question:1.Electric Circuits: Network graph, KCL, KVL, node and mesh analysis, star/ delta transformation; electromagnetic induction; mutual induction; ac fundamentals; harmonics, transient response of dc and ac networks; sinusoidal steady-state analysis, resonance, ideal current and voltage sources, Thevenin s, Norton s, Superposition and Maximum Power Transfer theorems, two-port networks, three phase circuits, power measurement . 2.Electrical Machines: Single phase transformer - equivalent circuit, phasor diagram, tests, regulation and efficiency; three phase transformers - connections, parallel operation; auto-transformer; DC machines - types, windings, generator/ motor characteristics, armature reaction and commutation, starting and speed control of motors; three phase induction motors - principles, types, performance characteristics, starting and speed control; single phase induction motors; synchronous machines - performance, regulation and parallel operation of generators, motor starting, characteristics and applications . 3.Power Systems: Basic power generation concepts; transmission line models and performance; underground cable, string insulators; corona; distribution systems; per-unit quantities; bus impedance and admittance matrices; load flow; voltage control; power factor correction; economic operation; symmetrical components; fault analysis; principles of over-current, differential and distance protection; protection of alternator, transformer, transmission lines neutral earthing, solid state relays and digital protection; circuit breakers; system stability concepts, swing curves and equal area criterion 4.Utilization & Control Systems: Principles of feedback; transfer function; block diagrams; steady-state errors; Routh and Nyquist techniques; Bode plots; root loci; lag, lead and lead-lag compensation; Heating - resistance, induction, dielectric; Welding spot, seam and butt; Electric traction speed-time curves, tractive effort; 5.Measurements: Bridges and potentiometers; PMMC, moving iron, dynamometer and induction type instruments; measurement of voltage, current, power, energy and power factor; digital voltmeters and multi-meters; phase, time and frequency measurement; Qmeters; oscilloscopes; 6.Analog and Digital Electronics: Characteristics of diodes, BJT, FET; amplifiers - biasing, equivalent circuit and frequency response; oscillators and feedback amplifiers; Combinational and sequential logic circuits; multiplexer; Schmitt trigger; A/D and D/A converters; 8-bit microprocessor basics, architecture, programming and interfacing. 7.Power Electronics and Drives: Semiconductor power diodes, transistors, thyristors, triacs, GTOs, MOSFETs and IGBTs - static characteristics and principles of operation; triggering circuits; phase control rectifiers; bridge converters - fully controlled and half controlled; principles of choppers and inverters; basic concepts of adjustable speed dc and ac drives.

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Question:A firm has the following average cost function: AC= 50+ 10/Q a) Show by differentiation that AC decreases indefinitely as Q increases. Give an economoic interpertation of this phenomenon. b) Write down the equation for total cost. hence, write down the equation for total variable cost and average variable costs. state the value of fixed costs. c) Write down the equation for marginal costs. Comment on the relatioinship between TC and MC in this example. 5stars answers

Answers:1. So why are you asking this economics question in the math section? 2. Parts a and b are completely independent. Which have you tried and how far did you get? If you don't know how to differentiate: http://en.wikipedia.org/wiki/Table_of_derivatives average cost = total cost / quantity so you can determine total cost as a function of average cost and quantity. From there: http://en.wikipedia.org/wiki/Fixed_cost And: http://en.wikipedia.org/wiki/Marginal_cost

Units, Measurements and Theory of Errors - Concept Builder 1

The measurement is any physical quantity, either fundamental or derived, requires a 'reference standard' called Unit. The international system of unit is SI unit, which has seven fundamental unit and it is rational coherent and metric. Learn more at www.youtube.com

Cardiomyogenic differentiation of Mesenchymal Stem cells (KUM2/9-15c)

Mesenchymal stem cells derived from bone marrow are capable of differentiating into cardiomyocytes. However the characteristics of the stem cells are poorly understood, and how the progeny of multipotent cells adopt one fate among several possible fates remains a fundamental question. A hierarchical model has been proposed on the in vitro differentiation of mesenchymal stem cells. Yamada and Umezawa show that mesenchymal stem cells in culture consisted of a mixture of at least three types of cells, ie, cardiac myoblasts, cardiac progenitors and multipotent stem cells, and suggest that commitment of a single-cell-derived stem cell toward a cardiac lineage is stochastic by a follow-up study of individual cells.

CalTech: Derivatives P2

In calculus (a branch of mathematics) the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a vehicle with respect to time is the vehicle's instantaneous velocity. Conversely, the integral of the velocity over time is how much the vehicle's position changes from the time when the integral begins to the time when the integral ends. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation is a method to compute the rate at which a dependent output y changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means that y is a ...

CalTech: Derivatives P3.

In calculus (a branch of mathematics) the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a vehicle with respect to time is the vehicle's instantaneous velocity. Conversely, the integral of the velocity over time is how much the vehicle's position changes from the time when the integral begins to the time when the integral ends. The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization. A closely related notion is the differential of a function. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Differentiation is a method to compute the rate at which a dependent output y changes with respect to the change in the independent input x. This rate of change is called the derivative of y with respect to x. In more precise language, the dependence of y upon x means that y is a ...

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